Yes, they are. However, there are special rules as to how one can enter a time loop. The first time that Jake visits Miss Peregrine's home over land, it is a ruin, having been destroyed by a German bomb during World War II. He later returns, but loses consciousness, and he is brought back to the house through a cave. That cave is actually the access point to enter the loop, so he finds himself at the house as it was in 1943. When he leaves the house, he does so over land instead of the access point in the cave, so he remains in 1943; he is then brought back to the house, and later returns to his hotel via the cave, ending up in 2016 again. Later, Mr Barron thanks him for showing him the access point, because he needed it to find the house.
When there is no one to reset the time, then the loop closes, and the area will progress into time from the reset point again. This is what happens at Miss Peregrine's home near the end, keeping the children stuck in 1943, and Jake unable to return to 2016.
However, there is a loop in Blackpool, established in January 2016. If they go there in 1943, they will find its access point that will take them to the loop in January 2016. Since the children go out of the loop again at the end, they return to 1943; Jake stays, and as the loop closes, he finds himself in January 2016 again.
The trick he does at the end is simple: he locates a few other loops that go to a time in the past, enters them through their access points, but exits the areas via other routes, so that he can remains in that particular era. All he needed to find was a particular loop that was close enough to September 1943, enter it through the access point, and leave it through another way.