Is it at all possible that other senators were asked to not share anything but that the two people you mentioned made some special arrangement, perhaps to drum up American popular support?
No, that idea doesn't pass the smell test. They're minority party representatives, and my understanding is Cruz (at least) has a reputation for being obnoxious and selfish, even among his co-partisans. There's no reason to think those two would get some kind of special permission, and plenty of reason to think they were being careless and/or selfish.
I lived in both Ukraine and US. They barely know what "senator" even means, yet alone know their names. Most people cannot say how many major political parties there are in US, they have their own parties. I'm pretty sure even Ukrainian president doesn't really care about US internal politics, only about external.
Ukrainian people: maybe; Ukrainian president: absolutely not (and there's was a great example of how the two can intersect just a couple of years ago). An understanding of a country's internal politics is vital to understanding, predicting, and influencing its external politics.
A smart Ukranian politician would consider American sentiment since they want our help