New Tube Owner

Sometimes a tube may have an internal short or bad connection. A cold solder joint to the tube socket could cause distortion/noise. Any of those problems could potentially be corrected by manipulating the tubes as you did, though it would be a temporary solution. If the problem recurs: try tapping each tube gently with a pencil. If it's a tube you can generally tell. Wiggling the tube within the socket will reveal a bad socket or connection there. If it never recurs: count your blessings. No- tubes will not have obvious distortion/noise during burn-in.

If I were you, I'd start fresh with a whole new set of tubes. That way you're ensuring maximum sound quality and not relying on the integrity of the existing tubes. I bought my amp used and almost all of the tubes were on their last legs when, to my surprise, the entire left channel cut out.

Could have been oxidation on the tube / socket contacts, just like any other connection.

Sometimes, the pins on the tubes MAY have a slightly loose fit in the tube socket. Trust me, this has happened many times to me...don't worry, unless it happens again. Then I can take you through "the drill"!