West Brom have pulled clear of danger since the Welshman took charge last month, losing just once in six league outings to move up to 14th, while also booking a place in the quarter-finals of the FA Cup.
However, with Saturday's opposition riding high and challenging for a top-four berth, Pulis has warned there is no room within his squad for complacency.
The former Stoke City boss refused to get carried away in Thursday's pre-match news conference, despite his side's form and the excitement surrounding next week's cup tie against Aston Villa.
"Come see me at the end of the season, when we've stayed up hopefully," said Pulis, who could be without Saido Berahino (knock) and James Morrison (hamstring) this weekend but hopes to welcome back Victor Anichebe after a groin problem.
"Then I'll talk about [the turnaround], but we're still miles away from staying up, we're still in a dogfight with every other club in the bottom eight or nine in the Premier League.
"Until that happens, I certainly won't be talking myself or the team up. We've still got 12 games to go and eight or nine clubs are battling to stay in the Premier League.
"I hope and pray we're one of those to stay up, but we're still in a dogfight."
Ronald Koeman will hope to see his team bounce back from a frustrating outing last time out against Liverpool, as their European aspirations were dealt a blow with a 2-0 defeat at St Mary's Stadium.
Koeman expects West Brom to afford Southampton a good deal of possession.
"I watched two of their games in the last few weeks and it's normal when you come in with a new team you try play out of a defensive organisation," said the Dutchman.
"It is not easy to score against them, there's not a lot of goals in their games and their opponents always have a lot of ball possession but it's not always about ball possession.
"And they are very strong at set-pieces. That is a big quality of theirs.
"I think it's one of the qualities of the manager [Pulis], to put a very good organisation in the team. They fight to avoid relegation and they fight for every point."
Southampton will be without Toby Alderweireld (hamstring) on Saturday, together with long-term absentees Jay Rodriguez (knee) and Emmanuel Mayuka (groin).
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