I arrived exactly at their cut off time is a correct grammar?

The grammar is technically correct, but it's a bit awkward. Here are some ways to improve it:

* More natural: "I arrived right at their cut-off time."

* More precise: "I arrived at the exact cut-off time."

* More emphatic: "I arrived precisely at their cut-off time."

The choice of phrasing depends on the context and the desired tone.