Lately CX seems to be going downhill in terms of reliability. On a recent trip to Taiwan via HKIA, all 4 flight segments were delayed, longest was over an hour.
Depends on aircraft scheduling, if it is the same plane for SIN - HKG and HKG - TPE, the HKG - TPE would definitely be delayed. Also, if there are many connecting passengers, they might also delay the HKG - TPE flight to take in all the passengers from SIN - HKG, and vice versa. You should be glad you make your connection despite the delay, instead of having to spend 1 night at HKG and waste your bookings/planned itinerary in TPE further. There might be other flights to accommodate too.
For example, I was on UA NRT - SFO. There are only 2 UA flights a day for that day. The first flight was cancelled due to non-operational plane. I was on the second plane and our flight was delayed to accommodate as many passengers from the previous flight if possible. Similarly, previously due to H1N1, incoming flight LAX - NRT was delayed, plus they boarded and checked all passengers' body temperature before allowing all the disembark, so taking much longer than usual. In the end, I disembarked at around the departure time for the NRT - SIN. They delayed the flight slightly for all passengers on these incoming flights.