I haven't had many problems with Evertonians over the years.
Most stemmed from the FA Cup QF in 1966. That went to two replays before Everton won 2-0 at Molineux. The first match at Maine Road (0-0) passed without major incident despite a 63,034 full house. The replay at Goodison was also 0-0 with a crowd of 60,349.
There were incidents with City supporters throwing cushions from the upper tier of the stand at the Everton fans below. We were on the upper tier and seeing a group of angry Everton supporters waiting at the bottom of the stairs, we reacted by walking down the stairs chanting Everton, Everton!
The second replay at Wolves attracted a decent crowd of 27,948. The Cup was not really a priority for City that season with promotion being the main objective. City had already had replays with Blackpool in the Third Round and Leicester City in the Fifth Round, so three Cup matches against Everton was not ideal preparation for the run-in.
Everton were due to play United in the SF. Leaving Molineux, we saw a group of Everton fans and wished them well in the match against United. They told me to piss off! I will not do that again.
Everton eliminated United in the SF and then went on to come from 2-0 down to beat Sheffield Wednesday 3-2 in the Final with an unlikely two goals from the 21 year old Mike Trebilcock. He only played 11 League games for Everton and scored three League goals before moving on to Portsmouth, Torquay, Yeovil, and Weymouth.