Pronunciation here may be closer to tinyaam. Can also be said as tenyaam in 'Iipay.
The -m here was probably once the -m different-subject suffix. In modern usage, tiinya is a Tiipay noun for "night" and tiinyam, with the "m", is the Tiipay verb meaning "it is night". In 'Iipay, tinyaam is only used as the adverb, "last night".