Something important to know about the writings of TV shows and movies in (almost all genres) but to keep things brief Sci-fi and Fantasy and their plot points.
Is that there is always a certain demand of suspension of disbelief required for them to function.
With that said, Fear the Walking Dead is a show about magical zombies with incredibly inconsistent stages of rotting causing the world apocalypse...small things like a diesel engine keeping the cooling system of a reactor is by far closer to reality then the rest of the show...albeit, unlikely, like you mentioned.
To go into this plot point a bit, according to nuclear-power some of these pumps can require up to 6 MegaWatts each....so yeah, a tiny house hold generator (which the largest I can find was a mere 150kW definitely wouldn't hold up....but that doesn't matter....its the point that counts.
As far as death by radioactive zombies go, it mostly goes by REM count and our characters having highly radioactive materials inside/on them...the show is using the idea that contaminated zombies (not irradiated) covered/soaked in Fallout/radioactive things are walking death sponges.
With medical attention, radiation exposure is survivable to a 200 rems acute dose exposure. If a group of people is exposed to a 50 to 59 rems acute (within 24 hours) radiation dose, none will get radiation sickness. If the group is exposed to 60 to 180 rems, 50% will become sick with radiation poisoning. If medically treated, all of the 60–180 rems group will survive. If the group is exposed to 200 to 450 rems, most if not all of the group will become sick. 50% of the 200–450 rems group will die within two to four weeks, even with medical attention. If the group is exposed to 460 to 600 rems, 100% of the group will get radiation poisoning. 50% of the 460–600 rems group will die within one to three weeks. If the group is exposed to 600 to 1000 rems, 50% will die in one to three weeks. If the group is exposed to 1,000 to 5,000 rems, 100% of the group will die within 2 weeks. At 5,000 rems, 100% of the group will die within 2 days
I would almost even say, the leaking of the containment is something that is quite realistic, when looking at the failures of humans in building complicated dangerous things we can find many examples of things going poorly.
Your issue is a direct symptom of the Reality is Unrealistic.
When exposed to an exaggeration or fabrication about certain real-life occurrences or facts, some people will perceive the fictional account as being more true than any factual account.
This is known as an "Orange Box" in television and movies, named after the "black box" of airplanes which are actually orange to make them easier to spot.
But with that said, your question was about containment systems not leaking. An Important thing to know about the containment systems is how they work.
During normal operation, the containment is air-tight and access is only through marine style airlocks. High air temperature and radiation from the core limit the time, measured in minutes, people can spend inside containment while the plant is operating at full power. In the event of a worst-case emergency, called a "design basis accident" in NRC regulations, the containment is designed to seal off and contain a meltdown. Redundant systems are installed to prevent a meltdown, but as a matter of policy, one is assumed to occur and thus the requirement for a containment building. For design purposes, the reactor vessel's piping is assumed to be breached, causing a "LOCA" (loss Of coolant accident) where the water in the reactor vessel is released to the atmosphere inside the containment and flashes into steam. The resulting pressure increase inside the containment, which is designed to withstand the pressure, triggers containment sprays ("dousing sprays") to turn on to condense the steam and thus reduce the pressure. A SCRAM ("neutronic trip") initiates very shortly after the break occurs. The safety systems close non-essential lines into the air-tight containment by shutting the isolation valves. Emergency Core Cooling Systems are quickly turned on to cool the fuel and prevent it from melting. The exact sequence of events depends on the reactor design..
I won't go very much in depth of that entire system, but I definitely count a lot of failure possibility points in that description....not to mention there is quite a large list of things going wrong with nuclear power generation
One of the first ones from Canada being:
The NRX accident. A hydrogen explosion occurred in the reactor core due to a cascade of malfunctions and operator errors. The world's first major nuclear reactor accident.
And From Fukushima, (which actually I originally found many possible references to their containment systems leaking, I decided not to post their references because I couldn't find a credible source) The Guardian, and Tepco says:
"When looking back on the accident, the problem was that preparations were not made in advance," Tepco's internal reform taskforce, led by the firm's president, Naomi Hirose, said in a statement on Monday.
The company could have taken steps to prevent a catastrophic accident by adopting more extensive safety measures, the statement added.
Tepco's about-turn came after an independent panel of experts challenged its claim that it could not have foreseen the up to 14m high waves that swept through the plant, knocking out its backup power supply and causing three of its six reactors to melt down.
On top of that, there are other leaks at Fukushima.
In Conclusion, if one wanted to explain away the leak, one could easily do my Plot Mathemagics. (tm pending)