To reproduce:
1. Open attached project
2. Open scene 1
3. Select Blue and Red materials
4. Increase their emission intensity
5. Notice that one of the materials got its emission color overriden

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Rechecking:

This is actually a by design behaviour, when selecting multiple elements and editing inspector both values are set to the same value. It's misleading because the float field of emission is calculating the color, so essentially setting both their colors as the same.

Closing as by design