Velicí is always prounounced as velicí, only in the nonstandard Common Czech one can use use veliký even for masculine animate nominative plural.
For the standard Czech declension see https://en.wiktionary.org/wiki/velik%C3%BD#Declension
Interesting. So it is my hearing that is not attuned to the Czech spoken language yet. I will keep on trying!
I am curious about the difference between velici/velci, velika/velka, veliky/velky. I used "velci" in referring to "tall boys" several exercises ago but it was marked wrong and "velici" was put in its place.