You are.
You need PZ, not I, for a PlusPoints upgrade (although if I>0, PZ should also be >0). However, the reason that you were being charged here is that you had an upgrade that had already cleared. The rules do not allow you to go back after your Polaris flight has cleared and extend the request to your connecting flight. One person has reported repeated success doing that anyway, but the rules are quite clear -- if you request PlusPoints multiple times, you will get charged multiple times.

(Also, I'd be surprised if you had a fare break at ORD on your flight, as nearly all UA TATL fares disallow end-on-end connections to domestic flights -- they want to be able to offer a sale fare on, e.g., ORD-LHR without offering it to the rest of the country too).

As for the actual rule -- it gets really complicated. If you have a stopover, you need multiple upgrade instruments. If you have a fare break that would not be a stopover if you were through-ticketed, you do not need multiple instruments. If you have a fare break that would be a stopover, but the departure is the same calendar day, YMMV, but I'd expect that the computer would price it as a single instrument. If you do not have a fare break, but you do have an overnight transfer, the computer will (IME) require two instruments even though it's a through-fare; there are reports of people successfully getting an agent to process this with a single instrument. (Example: AUS-SFO / overnight / SFO-HKG; it wanted two instruments even though it was an AUS-HKG through fare).

Oh, and incidentally, multi-city search and broken fares are only tangentially related. UA will sell a broken fare on a regular round-trip search, and it will sell a through fare on multi-city search. However, I do agree that occasionally, UA's pricing system seems more likely to find a broken fare when using multi-city search.