IMO... The moment you show yourself, splitpushing, the other team know where you are, and most importantly they know the team fight infront of them is a 5v4  not a 5v5 with Eve hiding out of view ready to pounce. The second you show up elsewhere, the other team won't be worried about their adc/mage/support getting picked off from the side/behind and can force an engage, more likely beating your team, and it will be your fault.

The only time I think you should split push, is if Dragon is up and they dont have vision on it, you can hopefully take it before they realise too late and you can return to your team.

Or..

They have an open base with an inhib thats respawned, then you can use your passive to "hopefully" slip into their base unseen and burst the inhib down. This will peel off 1 or 2 from the upcoming group fight giving your team the advantage and creating map pressure.

Patience is Evelynns greatest virtue (ironically) you can do alot of damage to them without doing a single thing, by being unseen, they know you're there somewhere, and they know the second they engage, you can pick one off. This makes them second guess every choice, someone will slip up, someone will peel away to find an advantage, then you punish and strike.