ok, here’s my stab at this.
the eurodollar futures (EDF) are meant to represent you loaning money. So you buy an EDF, it means you are locking in a rate to lend money at a set rate for 30 days some time starting in the future (say 3 months from now). At least that’s what the contract is meant to represent.
so if rates are 5%, the interest you are going to earn at the end of that 30 day loan is going to be $1M * 5% * 30/360. If you buy this contract and rates go up by 0.01%, you lose $25. That’s the way the contract works.
The thing is, if you actually loaned someone money for that 30 days, yeah you would make that $1M * 5% * 30/360, but that interest is paid at the end of the 30 days. There is NO discounting effect calculated like there is when you do a FRA.
So EDFs don’t actually reflect the economic reality of what you would gain/lose when you loan/borrow money and rates move. This is why they are not a perfect hedge.
To your question, why does it work for t-bills and not EDFs. The EDFs don’t discount back the interest cash flow to your futures expiry point, whereas the T-bills futures do (a future on a discount security)
I’m no expert but this is how I understand it.