There is a toilet that fouls every now and then. It can overflow if there is a second flush after plunging. So I will shut off the feed and try a flush. If not successful, I will fill the tank by hand and try it again. This upsets someone in the family who claims it can cause bubbles which will cause another foul in a short while, and blames me for using this method.
How could my actions cause any fouling?

It can't cause bubbles.

Don't fill the tank, just pour a bucket of water directly into the bowl.

The elephant in the room...

>There is a toilet that fouls every now and then. It can overflow if there is a second flush after plunging.

You have a clogged drain line, and plunging is giving you only temporary relief. It is likely partially clogged, then gradually gets completely clogged, then plunging restores it to partially clogged. This will likely get worse over time.

>This upsets someone in the family...

It's probably time to call a licensed plumber, so as not to upset someone further.

You can snake it yourself. If you're ambitious you can unmount the toilet and snake directly. Maybe you'll find a diaper or a bolus of 'flushable' (not!) wipes. Maybe a bottle of 'Green Goblin' will work. Bubbling is a different thing, a failure of suds relief from fixtures higher up. Are you describing something other than an incomplete flush?