Hello Sasha. Tricky, that one. Your logic is sound, but I don't think it sounds idiomatic when you use the simple past.
In this sentence, with a few tweaks, Andrew is the cause of the employment-related ennui:
- After Andrew came into my life, I began to move from one dead-end job to another, without much idea of
what I really wanted in life.
In this one, he may actually be the person who saves the writer from the sorry state of affairs:
- When Andrew came into my life, I was moving from one dead-end job to another, without much idea of
what I really wanted in life.
So in relation to the test, I would say both are possible, grammatically; but the second -- the past continuous form -- makes more sense in terms of the semantics.
Take your pick. ;-)