I'd like to know who supplies the estimates for the wallets with fee control.
I would guess it's just based on the last blocks, similar to what Bitcoin Core Recommends.
The site says:
How is the delay predicted?
The predictions are based on blockchain data of the last 3 hours, as well as the current pool of unconfirmed transactions (mempool).
First, a likely future mempool and miner behavior is predicted using Monte Carlo simulation. From the simulations, it can be seen how fast transactions with different fees are likely to be included in the upcoming blocks.
The predicted delay shown here is chosen to represent a 90% confidence interval.
I haven't tried this but if you use electrum, try setting it to be 0.5mb from tip as the fees will be lower and it should confirm within 4 blocks if you're really unlucky (if you're not in a rush use 1 sat per byte as long as its less than about 16mb from the tip it should confirm within a day).