>Apparently the tubes need to burn in? Or is that a myth?

In my experience this is only the case if your tubes are humming. Sometimes new tubes hum out of the box and after 24-48 hours of simply leaving your amp on (in my case without the power tube) the hum can disappear. On some tubes I was able to get rid of the humming completely, but with some others it didn't work.

Some manufacturers say that their tubes sound best after 100-200 hours of use, but honestly, just enjoy, lean back and if there's change then see it as a nice bonus. I wouldn't leave the amp running because tubes don't work forever and can become microphonic and whatnot. My Tung-Sol 6SN7GTB I bought used started whistling like a tea kettle after a while, as an example.

Btw in my experience I haven't noticed a tube changing in sound yet and I've tried a few.

Edit: getting rid of stock tubes is almost always a good plan though.