This scene appears in the source novel by Ian Fleming, albeit with a paper note rather than an SMS.
At four o'clock Bond was about to call for the bill when the maitre d'hotel appeared at their table and inquired for Miss Lynd. He handed her a note which she took and read hastily.
'Oh, it's only Mathis,' she said. 'He says would I come to the entrance hall. He's got a message for you. Perhaps he's not in evening clothes or something. I won't be a minute. Then perhaps we could go home.'
Suddenly the note to Vesper seemed odd to him. It was not the way
Mathis would do things. He would have asked them both to join him at
the bar of the Casino or he would have joined them in the night-club,
whatever his clothes. They would have laughed together and Mathis
would have been excited. He had much to tell Bond, more than Bond had
to tell him. The arrest of the Bulgarian, who had probably talked some
more; the chase after the man with the stick; Le Chiffre's movements
when he left the Casino.
It's also pretty notable that while Vesper and Mathis are both ostensibly on the same side and share a mutual contact (Bond) there's no obvious reason why he'd be touching base with her instead of him. This explains the second part of your question; Bond is leaving the restaurant, not specifically to follow Vesper but to go and see Mathis.
When added to the fact that he's still trying to puzzle out how his ability to read Le Chiffre's "tell" failed (something that only Vesper and Mathis could have disclosed) it all seems a bit suspicious and certainly worthy of his attention.
For the record, he probably would have realised all of this sooner if he hadn't nearly died a few hours ago.