Attended a Purim Seudah tonight at a Sephardic shul where most of the attendees are Israeli. They only made noise during three (maybe four?) times Haman's name was mentioned. I am aware of the teshuva saying "no noise", but can't find anything explaining "sometimes." Is there a soource for this concept?
There are various customs about making noise when Haman is mentioned. Since you mention that it occured more than once, it sounds like the Chabad custom.
While most congregations allow banging each time Haman is mentioned, others have the custom to do so only when his name is mentioned along with an accolade, such as “Haman Ha’agagi” or “Haman Hara”.38 Some only bang when hearing Haman’s name during the segment which discusses the demise of Haman’s ten sons.39 Yet others have the custom to do so only at the first and last mention of Haman in the Megilla,40 or only those references to Haman which discuss his downfall.41
38 Aruch Hashulchan 690:24, Sefer Haminhagim Chabad
39 Ketzot Hashulchan 690, Nahar Mitzrayim;Purim, Minhagim of Worms 2:259
40 Ben Ish Chai;Tetzaveh
41 Emek Bracha Purim p.246
As Sabbahillel mentioned, it may have been based on some pattern. I have heard of many of those combinations (although I've never heard of only banging for only "Haman Hara", which occurs only once during the Megillah, so definitely wasn't your case).
Most likely, it is one of two options:
They banged each time it mentioned Haman...Ha'agagi, which occurs 5 times in the Megillah (3:1, 3:10, 8:3, 8:5, 9:24).
What may be happening is that there was an agreement between the Ba'al Koreh and the Gabbaim (or congregation) to only stop at a few "Haman"s to save time, in which case there may be no pattern at all. I know that I have personally done this a few times.