Deila encountered several rocky situations during his first few months at Celtic Park, especially after his side were knocked out of the Champions League at the qualifying stages, as well as the occasional underwhelming result in the Scottish Premiership.
Now, though, very little is going wrong for Celtic's Norwegian boss.
The Bhoys are on fire domestically and, even after being knocked out of the Europa League by Inter Milan, Deila's men acquitted themselves exceptionally.
That has all led Strachan to heap praise on the 39-year-old, who he feels has now developed a strong rapport with supporters.
"He understands what it is all about now," the ex-Celtic and current Scotland manager said.
"After a month or so in Glasgow he will have no idea what had hit him. But now his team are playing well, the games against Inter were good and now he is enjoying it.
"You have to be able to handle the stress and deal with the knocks but you are always going to get time here. It is not revolution here - it is all about evolution because there are people here who have done a good job here in the past. The fans are enjoying him too and he's got a good relationship there."
If anyone knows what they're talking about, it'll be the former Celtic boss, who won three league titles during his time as a club manager in Scotland but never won the treble.
Deila, meanwhile, knows he is on the cusp of a special debut campaign at Celtic Park - something the 4-0 win against Aberdeen has drawn the Hoops a big step closer to.
Next up for Deila's men are St Johnstone on Wednesday night, when the champions can move nine points clear of the Dons.