At least as it applies to the Pacific;
Definitely; despite the seasons not appearing to change as dramatically, the stars in the night's sky do alter throughout the year. For instance the Makahiki in Hawaii is sometimes referred to as a new years celebration; but Hawaii was not alone Tahiti and elsewhere in Polynesia celebrated ceremonies marking the rise of the Pleiades Star Cluster (though of course they had their own names for it).
That said; there are definitely noticeable seasons at least in the equatorial/tropical Pacific though the changes appear slight to people used to more dramatic shifts.
While most tropical climates do not have noticeable differences in temperature from one part of the year to the next, the same cannot be necessarily said for rainfall. Apart from those right on the equator (and even then, East Africa is a notable exception), most tropical climates do have a wet and a dry season, or times of year in which the prevailing winds blow in one direction as opposed to another. These can act as a measure of time in the same way as temperature seasons do in temperate or boreal climates.
Alternatively, one could have measured time by the moon, eg. one could have said that an event happened 'three full moons ago' (which is in fact where the definition of a month comes from), or through which constellations were present in the night sky at any given time.
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