is it common for them to have mutual citations, in the sense A is cited in B and B is cited in A?
It is common enough in my experience, I've ended up with such reference chains with other authors. You'll know that often the core idea/initial draft of a paper is available in preprint form long before the final version's official appearance in print. The situation I've seen is:
Preprint A appears -> Preprint B cites A -> Article A goes through enough rounds of revision to delay it until after B has a proper acceptance/DOI -> Final version of article A cites final version of B, final version of B cites preprint version of A.
But there are of course other mechanisms for this to happen.
Does it not create (an initial) confusion on which work is done first?
This wording seems off to me. What creates confusion is the publication process's logistics and timing and the lack of detailed historical notes on the development of articles and ideas. But yes, if you have mutual references in two papers, it's harder to use those references by themselves to temporally date which paper was first publicly available. This is in a genre of problem which has been very common for the last few centuries. If you want to figure it out, I'd suggest arxiv as the next possible resource.