A 4-1 Ashes defeat, with Australia retaining the urn after just 11 days of cricket, has put an extra emphasis on the T20 World Cup although England have booked a semi-final spot with a match to spare.
Southee, who played alongside McCullum 170 times for New Zealand and joined his backroom staff at England on a rolling contract last May, insisted his former teammate is focused on the task at hand.
"Baz is just Baz," Southee said. "I have known him, played a lot with him and get on with him very well. But one thing with Brendon is he is the most consistent guy I have ever come across.
"Nothing really changes from him. He believes in what he believes in. He's been very consistent with his behaviours and it's been no different here.
"He just wants guys to do well, he wants the team to do well and that hasn't changed since he was a player and now as a coach."
England will seal top spot in their super eight group if they follow up wins in the last few days over Sri Lanka and Pakistan in Pallekele by beating New Zealand at Colombo's R Premadasa Stadium on Friday.
Southee - who played 394 times in all formats for New Zealand, including taking 391 wickets in 107 Tests - admitted he will find being in England's dressing room "a little bit strange".
But he's enjoyed working with Jofra Archer, who started the tournament with combined figures of 2-80 in eight overs against Nepal and the West Indies, having just returned from a side strain.
Since then his figures read 15-0-111-8 in four games and his 90mph-plus pace has discomforted several batters, with Southee convinced Archer could be peaking at the right time.
"Looks like he's getting better and better so that bodes well for the next few games," Southee added.
"It's been brilliant to see how he goes about his stuff. He absolutely loves cricket, loves bowling, so it's been great to work alongside such a great bowler."
New Zealand head into the England showdown, determined to get the win that's the only way to avoid leaving their semi-final hopes at the mercy of rivals and net run-rates.
If England, who are already through to the semis, beat New Zealand, then Pakistan will still have a chance to make the last four provided they beat Sri Lanka on Saturday, and end with a better net run rate than the Black Caps.
"It's not doom and we're not dead if we don't win," coach Rob Walter told reporters on Thursday.
"But certainly we leave it up to external factors then and it is out of our own hands."
With Reuters
