Q: Can a submission be in production and at the same time be assigned to a reviewer?

This seems like a slightly unusual situation, A few questions that are relevant here: How long has it been since you first submitted your paper to Journal A. How long was it with Journal a before it was transferred to Journal B? Did you receive any communication from the journal about the transfer? Also, were you informed about the transfer to Journal A again? In short, have you heard from the journal about the transfers? Also, did you track the status of your article in Journal B? When you say it was reviewed, did you find out if it was peer reviewed?

In this case, it appears as though your paper was transferred to Journal B for valid reasons, where it was evaluated by the editor who may have thought it would best be handled by the origina journal - journal A. The "under review" status you may have seen with journal B might have indicated the editorial evaluation instead of the actual peer review. So it is likely that journal A will now undertake an actual peer review of your paper. This is one possibility

The other possibility is that your paper has been peer reviewed by journal B but will be made publiclation ready by journal A. 

I suggest that you write to the journal - journal A - and request a clarification, especially if it has been more than three months since you initially submitted your paper to the journal.

You might also be interested in the following handbook that addresses specific questions researchers have about journal decision making and the timelines around it:

Keep calm and wait: A guide to understanding journal statuses

Recommended reading:

• How long should I wait for a response from the journal?
• Tracking your manuscript staus in journal submission systems
• How to communicate with the journal editor?