It's a shame Everton put out that initial statement. They could have easily kept their misgivings to themselves, and it has reflected badly on them as a club. Hopefully, they will learn a lesson from it.
Spurs probably saw the reaction, and their statement reflected this. (This isn't to say Spurs would have acted differently had they not had the benefit of commenting after seeing the Everton reaction).
In my view, Everton FC made a misjudgement. Ancelotti to his credit has gone some way to making amends. But let's not judge the entire Everton club or fanbase as evil, on the back of one error of judgement.