What a pretty colour!
I think that all these 'it's not ideal-s' are adding up and you could end up with a serious problem if you don't address things now.
All 3 of mine have moments where they feel a bit frisky and swim about like mad, but thats normal for them, and I know the tank parameters are ideal, because I'm obsessive about it.
I would follow Julias advice about taking him out for a while and getting the tank perfect before introducing him back into it.
Looking at the vid - I can't tell how much of that current is caused by axie swimming about - could you post a vid when he's still, too? That might not be helping.
Re: Temp - Just because a pet shop does something wrong, doesn't mean if we do it slightly less wrong it'll be ok!
As a sort of side note, his tank looks a little bit, well, boring! He could even be trying to find somewhere to hide. I know you have the pipe, but it's white, and therefore a good shelter, but he might not feel very hidden!
I know mine absolutely LOVE small, dark spaces. I don't think claustrophobia is something axies have to worry about, haha!
Have a look around on the forum at other peoples tanks, and see if theres anything you fancy trying for his tank. Dark spaces, hides, plants etc - I also think you'd find your axie a thousand times more entertaining than he already is, they don't half do some funny things (dangling from plants by a toe etc). So think 'lake bottom' and I reckon he'll thank you for it.
Make sure it's easy to clean though, I think we've said before, tons of pebbles is a nightmare. At the bottom of a lake there'd be other critters to clean this stuff up!
So, as I was saying, anything that isn't ideal, should be addressed, and get him out of that unhealthy water until it's under control. Having a cycled tank is good piece of mind. Plus, I'd stop listening to ANY advice that pet shop gives you, unless it's repeated on here!
Hope that helps, you've got a gorgeous axie there, makes me want to traipse across Scotland to find a golden, so keep him happy and healthy (and me jealous) for a very long time!