Not always.
But most of the time. Some examples:
- Magikarp is water type and red. This alongside several other fish Pokemon.
- Nidoqueen, a ground and poison type, is neither brown nor pink, rather blue.
- Reshiram is fire and dragon, but it white, not red.
…and several other examples. As of such, pokemon just happen to have colours that depict their type, but are not based off them.
Hope I helped!