These are just portals - they're nothing to do with time or the time stone as no travelling through time is occurring. These portals are no different from the portal used to bring Tony Stark to the Sanctum Sanctorum at the start of Infinity War. They're also the same portals used for capturing/releasing Loki and transporting Loki and Thor to Odin during Ragnarok.
Professor Hulk snapped his fingers, this bought everybody back to life at the location they were dusted. The team on Titan reappeared on Titan immediately after Hulk's snap and then travelled back to Earth. There is no time travel involved.
As for what is going on with Doctor Strange's timestone - it was destroyed already. Thanos destroyed it at the start of Endgame. The timestone in play right now comes from a time predating Doctor Strange becoming a master of the mystic arts and at this exact moment in the movie, the team's intention for the stone is to return it to the past.