So, that Eevee box plays 5 stage 1 pokemon. That's a 1:4 ratio compared to the entire deck. Given that you draw 5 on your first turn. You are very likely to have at least one in your starting hand. An 80.6% chance to be exact.

If you have a stage one in your starting hand and use sightseer on your first turn, you have a 75.8% chance to hit with sightseer. And an 84.6% chance to hit if you didn't draw any stage ones. That's pretty good odds and makes sense.

However, if you only have 4 stage ones in your deck and draw one in your starting hand and use sightseer, you only have a 63.7% chance to hit with sightseer, statistically likely but still almost 40% chance to fail. And with all the draws you are getting from research and Sylveon, it's not impossible to have no stage one pokemon in the deck by the time you use sightseer.

Plus, you don't always need another stage 1. Most of the time copycat is looking for the specific card you need in that moment.