I'll edit the lack of LTE - this was data someone else contributed

What phone do you have so I can verify it wasn't an device issue. Digicel *IS* HSPA on that network - the way HSPA works is a long as UMTS is authenticated it will connect to HSPA. I have heard of Digicel in early days of UMTS and then HSPA doing IMEI blocking on device mfr ranges that weren't tested on their network (a few other networks like Chunghwa in Taiwan did the same). Symptoms were auth on UMTS or HSPA then immediate drop down to a lower perf network (e.g. UMTS or GSM). Really odd that their auth implementation would even allow it to connect at all.