Della, I think Bomareas are closely related to Alstroemerias but I am not sure
The one in the link you provided - it's the very first time I see a picture of it (though not exactly what I would call a beautiful flower/plant
Check Bomarea ovalliensis (Garra de León /Lion's Claw) (Chilean endemic species) at this Google Chile link: https://www.google.cl/search?h...
Re. your Alstromeria aurea/aurantica, could it be that plants on different maturity stages bloomed (just one), providing the sensation they are recurrent bloomers? The other possibility is: when you pull (not cut) the flower-stem, this often causes the division or the rhizome, splitting it into two plants. Maybe one plant or both produced from this separation could then bloom?
People usually think of Alstroemerias as having tubers: wrong! It is (in some cases a tiny) a horizontal rhizome with fleshy (very brittle) roots. Some times, it is very hard to distinguish the rhizome, but it is there.
When I was an active member at DG, I posted a picture that clearly showed this for one of our native (most of the endemic) Alstroemeria species. Unfortunately, I do not remember which one