Fremantle extended their club-record AFL winning run to 11 last Saturday with their away victory over two-time defending premiers Brisbane.
The Dockers are yet to win a premiership in their 31-year history, but the talk in the west now is about "Flagmantle".
Longmuir is pleased that so far this season, the club is showing a greater maturity around managing those expectations.
"It's a good place to be ... a good problem to be dealing with," Longmuir told AFL360 on Monday night.
"It's probably something I don't think we've dealt with overly well at our club previously.
"There have been times when we've won three in a row and 'Flagmantle' comes out, and then we lose one we should win.
"This group is maturing, we're able to get our feedback from the right places, we feel like we're able to pay every opposition the correct amount of respect each week and really stick to our process."
Longmuir was asked whether his side's run of form was raising expectations.
"What it's doing is building belief, and Brisbane are one of those sides who we've probably struggled against in the past - especially last year, they got a hold of us," he said of their massive scalp on the weekend.
"(It) was just a little belief built among the playing group and staff."
Longmuir said he was talking to his senior players "ad nauseum" about sticking to what is making them successful.
As for the excitement among Fremantle fans, Longmuir is rapt for them.
"They can get ahead of themselves all they want, for all I care, it's just important that doesn't creep in internally," he said.
A major highlight for the Dockers after their win in Brisbane was a surprise visit to their rooms by retired Fremantle great Nat Fyfe, who's living in the area.
The current Dockers made a beeline for Fyfe, who ended his glittering two-Brownlow Medal winning career at the end of last season.
"It's a shame that he's not around, but I don't think he would have any regrets - he got the most out of his body," said Longmuir, who added it was the first time Fyfe had visited the team this season.
"It was great to see the reactions of our players. They had no idea. He still means a lot to us."
Longmuir also made the pecking order clear among his side's key forwards - Patrick Voss, Josh Treacy and Jye Amiss.
"If you asked Vossy, he'd say it's him. He walks around with his chest out," Longmuir said when asked who was 'top dog'.
"But if you asked JT in front of Vossy, they'd both know JT is the man.
"And Jye just goes about his business. He's probably been the most in-form out of the three of them in the last month."
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