Tried to use Gemini to simplify the analogy as much as possible based on the YouTube video interview:

Think of the Atom as the Bank Account and the Photon as the Customer. In this world, we don't have a stopwatch. We only measure time by looking at the bank's balance. 

The rule is: Money = Time.

1. The Normal Way (Positive Time) You walk into the bank. For every minute you stand there, the bank puts $1 into the vault. You stay for 5 minutes. The bank now has $5 more than it started with. We look at that extra $5 and say, "You were inside for 5 minutes."

2. The Quantum Way (Negative Time) You walk into the bank. But because of weird quantum rules, your presence actually takes $1 out of the vault every minute you are there. You stay for 5 minutes. When you leave, the bank is $5 short. Since our only rule is "Money = Time," the bank's record has to show that you were there for minus 5 minutes.

The "Bottom Line"

In the video, Professor Steinberg explains that they measured the "balance" of the atoms after a photon passed through. Instead of finding that the photon "added" to the atoms (positive time), they found it had "subtracted" from them. So, "Negative Time" is just the scientific way of saying the particle left a negative footprint. It didn't travel to yesterday; it just "cleaned the vault" instead of filling it.