We have an old apartment building. It is wired with two-prong outlets fed by two-wire cable (hot and neutral, no ground).
When I test these outlets using a pen-style tester (the kind that "senses" current without actually touching the wire) both side give a hot reading.
The outlets work fine otherwise (appliances plugged into them work).
When I test the outlets in my home (with grounded outlets) one side tests hot, the other doesn't.
What's happening with the older outlets? Is this a problem that needs to be fixed? If so, how? Hopefully not by rewiring the entire building.
You should be alright. Some tickers will show what you describe. Mine does on occasion. If I put mine next the neutral wire in some outlets, it will show live. I have never worried about it. You are fine.