Advisor wants me to send manuscript to a potentially shady journal
Why not? A quick look at the controversy indicates that the disagreements were entirely around the editor-in-chief publishing his own papers in the journal, papers which were lightly reviewed + indulged in a lot of self-citation. This means:


It's only the editor-in-chief's papers that are affected; none of the papers by other authors published in the journal are;
Once the editor-in-chief changed, it's no longer a problem.


So even if the editor-in-chief was in the wrong (which is not certain), it should be fine for you to publish there.

If it still concerns you, note that Clarivate Analytics / Web of science still has the journal indexed, i.e. they think the journal still meets their standards, and it has an impact factor of (as of time of writing) 3.064 which is good for the field.