There are a couple points here that involve the different community perceptions of the other sites and processes.
First, there is the repost rather than migrate. When one has a question that isn't appropriate for one site, but is (in theory) appropriate for another site, it should be migrated rather than reposted. Because of questions of quality alluded to by Guvante's comment Programmers.SE isn't a migration target for StackOverflow as part of the close process. However, any question can be migrated to any site by moderators. Rather than reposting a question, one should instead flag it for moderator attention and ask for it to be migrated. They may say yes, they may say no. If they say no, work with people in chat to either get it answered (it may be a question that is best suited for chat rather than a Q&A site), or help you recraft the question so that it can get migrated.
Reposting a question rather than migrating it often leads to headaches and frustrations, especially when the question would be closed for a reason other than topicality. If a question is not constructive, or overly broad, or too localized on one site, it is likely the case that this is true of the question on another stack exchange site. This is where it is especially helpful to work with people in chat.
StackOverflow has the perception (or P.SE has the perception that SO has the perception...) that anything that doesn't have code attached to it is a question that should be on Programmers.SE. This is not always the case. As mentioned, these are questions that sometimes fall into other close reasons (too broad, too localized, or not constructive) and thus shouldn't be on P.SE. Other times they are questions that are appropriate for sites other than P.SE.
Programmers.SE has the perception that SO is the correct migration target for things that have errors in code (if it doesn't have errors, the perception is it belongs on CodeReview). There is also the perception that tool related problems belong on SO.
The 'tool related' is where your question falls into the migration juggling. There was no code, it seemed open ended and thus someone at SO thought that it would be best at P.SE. However, P.SE notes that SO has the part of the SO FAQ:
software tools commonly used by programmers
As such, a question about the tools belongs on StackOverflow.
At least, that is the perception of this P.SE user.
If in doubt, flag for migration and chat rather than repost.