mina, this is normal.
A bike will be stable when on the side stand and the bars to the
left.
The bike may appear to be a little unstable but it should not be a problem, that is unless you have a bent side stand or if something is broken or wrong. The bike (with the bars to the left) will be stable and will take a fair bit of "encouragement" before it falls, yet.......
When the bike is on the side stand and the bars are to the
right the bike becomes less stable (by alot) and is easily knocked over.
From what you have written I think all is OK.
Even thought I have said that the 'bike will take a fair bit of "encouragement" before it falls' does not give you licence to push and poke because the bike can and will fall.
Buy a rear stand for your bike and all should be great
I bought a 'Sharp' race stand and it works a treat. The bike is more stable & the bike will sit vertically. It also makes cleaning the chain & general rear end maintenance easy.
I hope this helps
Enjoy