This is always a topic of debate. The misconception is, if you evolve straight away, your Pokemon will have higher stats. While this is usually the case, the illusion becomes that the earlier you evolve, the higher stats you will gain.
Since Pokemon stats are all based on a fixed number for each evolution, the only variation between the same Pokemon's stats are from IVs and EVs and natures.
For example, let's take your Umbreon. Umbreon has the following base stats:
HP Base 95
Attack Base 65
Defence Base 110
Speed Base 65
Special Attack Base 60
Special Defence Base 130
Alright, let's assume you have two different Eevee, which evolve into Umbreon. One evolves at L30, while another one evolves at L60. Both of which have the same nature, EV and IV distribution. At L100 (or any level), both Umbreons will have exactly the same stats. This is because they are all based around the same base stats.
In conclusion, it doesn't matter when you evolve, because the stats for one Pokemon will always be roughly the same, the only differences being where you put EVs, and their IVs and nature.