I have noticed that when making a custom potion, the custom effects don't override the potion's default effect. E.g., when I use the command below, I get a potion that has invisibility as well as blindness, but as I customized it, it should only have blindness.
Here's the command:
/give @p minecraft:splash_potion 1 0 {CustomPotionEffects:[{Id:15,Amplifier:0,Duration:200}],Potion:"minecraft:invisibility"}
In 1.8, custom potion effects did override the default potion effect (which back then was provided with the item id, not the Potion tag).
This potion would only give you speed, but not fire resistance in 1.8:
/give @p minecraft:potion 1 8227 {CustomPotionEffects:[{Id:1,Amplifier:0,Duration:200}]}
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Wrong! That's 1.8! 1.9 changes potion data!
Reopened.

Confirmed for
15w42a I assume you want to get the potion name and that is what you use the
Potion
tag for. However in my opinion the way it is currently solved makes more sense than how it was solved in and before 1.8.
The Potion
tag indicates what "main" potion you get. In your example you expected to get a potion with blindness but the name "Potion of Invisibility". However this would be a contradiction. Instead Mojang should finally support Json for entities, tile entities and items so you can easily use a translate
json component for achieving the name "Potion of Invisibility".
They are additive.
Your doing it wrong.
the correct way
is this:
when you added Potion:"minecraft:invisibility" you told the
game to give you the potion with blindness AND invisibility
combined. Which If you want to have it blindness it's self,
just do