The Shrimpers' 2-1 win over Gillingham on Saturday equalled the club record for successive wins.
It is an impressive start to the season for the Essex side, who won promotion for the League Two play-offs last season.
Tilson said: "The three points were more important than a record but it is nice to have equalled it and we now want to keep that going.
"It was a tough match though - they don't play a lot on the floor - but everyone worked for each other.
"Our priority is still to stay in the division and the quicker we can get to 52 points the better, but things can change quickly in football and we can't afford to get carried away.
"We're still looking to consolidate and we will take a look at things at Christmas and review that."