The SIM card isn't capable of managing complex records. Due to its limited storage, it only holds one phone number per contact, and also misses other details.
So when your "old phone" allowed for multiple phone numbers with one contact while storing the data on SIM, it must somehow have used multiple contacts, and displayed them in a kind of "merge view" (had it used some own format to achieve this, your SIM contacts would have become incompatible with other devices, so that approach is unlikely). While that would be doable on Android as well, it's not a standard for good reasons: How to tell which contacts to merge? By their name? There might be multiple "John Smith" entries, not necessarily pointing to the very same person.
As long as there's no standard defined, implementations might differ and thus leading to different results – which is the most likely reason it's not done at all.