Our perception of time is primarily based on chemical cascades which operate with a clear resonant frequency.
I don't think a keener sense of time would affect expression until you get to some pretty far extremes. Our expression for the sense of time is sufficient for some pretty spectacular ranges:
We have language to describe the femtosecond realm, where we capture light in-transit, such as this apple lit up by a pulse train of different frequency lights:
We have words to describe the concept of the origin of the universe, and the inflationary period which appeared after it:
We can even describe precise time, such as the 0.0000000000000004 drift rate of an atomic clock
Our sense of time is quite fine tuned indeed!
However, one interesting place you might explore for your aliens is a distributed concept of time. Much of our ability to express nuanced concepts of time is based on having one "master" clock from which all others derive a reference. The challenge, of course, is how to synchronize to this clock. Your aliens might develop a strong sense of time before the hardware/wetware to synchronize to a single clock. In such a world, you would want to have a distributed sense of time. Very few parts of humanity have to deal with distributed time, so we have very few tools for it. The two most famous ones I am aware of are Vector Clocks and Lamport timestamps. The former is very powerful but hard to implement, while the latter is easier to implement but not as strong.
With such a distributed system, you would find the need to be able to express events which occur at different times, or even in different orders, according to the observer. This would create a lot of room for interesting language choices!