That's an interesting question. I found this on the portal after clicking my points balance in the top right corner (which also shows how many points you have at 1.25 and how many at 1).
"These points are eligible for 1.25x when redeemed for Chase Travel; however, they will be used first and automatically apply to any redemption you make—reducing the number of eligible points whether they’re redeemed for Chase Travel or something else."
So your Hyatt transfer will take the 1.25 points first.
If you happen to have another card that can transfer to partners, you could move it there instead.