Cosmos consistency after committee rotation

Cosmos is using Tendermint as its consensus protocol. Tendermint can be proven to be safe - the protocol can not generate two conflicting blocks. However, the proof is valid to a given committee. Theoretically, after switching to a new committee, if the new committee is not aware to the decisions of the old one it can make a conflicting decision.
How Cosmos/Tendermint solve it? Is there a hidden assumption that most members of the new committee are aware to all the decisions of the old one? Is it so since we expect committees to be somewhat static - the 150 nodes with the higher stake, so we expect changes in the committees to be small (only few new members each time we are updating the committee)?

The “committee” is always the set of x validators (can be set chain-specific) with the highest voting power (coins delegated to them). Changes to the committee are happening all the time, but are rarely drastic and game-changing. And since the committee is determined on a block-by-block basis it goes fast and flawlessly.

Blocks minted in the past are final and we move on, such that a new committee further down the line does not alter that block (the magic and charm of blockchain ^^).

LeonoorsCryptoman:

The “committee” is always the set of x validators (can be set chain-specific) with the highest voting power (coins delegated to them). Changes to the committee are happening all the time, but are rarely drastic and game-changing. And since the committee is determined on a block-by-block basis it goes fast and flawlessly.

Thanks! I assumed this is the case but wanted to make sure.

Lets create a committee to check the committee that decides who goes into the committee that checks on the fist committee =)