I think the main problem is your edit summary ('Tags updated'). Nobody not everybody seems to read tag excerpts, so the author of the question might not even know the [api] tag shouldn't be used anymore on Stack Overflow.
Also, React Native uses Node.js underneath, and many people synonymize tag 'npm' with tag 'node.js'. This might be the reason the author (or perhaps the ♦ moderator handling your flag) thinks this tag is appropriate. Even though the tags are (arguably) wrong, it might not be clear to the author why you are removing them. Suggesting the edit a second or third time won't help and might even be perceived as harassment by them.
A solution to this would be either to improve the edit summary, stating why this question shouldn't be tagged this way, or (as @rene suggested) add a comment.
Flagging for moderator attention is usually a last resort, even more so on a site like Stack Overflow where moderators handle thousands of flags each day. The more problems can be handled without their intervention, the better.
Note that if you would have 2k reputation, the edits would apply directly. The author of the question still has the option to rollback to a previous version; if that happens too often on a single post, a rollback war moderator flag is raised, with a similar purpose of your custom flag.
The OP is rejecting my suggest edit even when the post does not contain proper tags
Yes, I said the tags are wrong but in another post that OP deleted