Being discharged well after 1883 there should have been a record in document series WO97 at the National Archives, Kew; there are two exceptions to that (i) those who died in service, (ii) those that went on to serve in any capacity in WWI.
As I couldn’t find any record in document series WO97 for a Charles Murphy b c1868, Aldershot Hampshire he must have served in WWI too. You should check for any service or pension record for him on Ancestry, being discharged as a sergeant and going to serve in WWI even at home in either a training roll or the Royal Defence Corps he should have accumulated enough service to be awarded a long service pension..
The only way to check his regiment earlier in his service is to trace the children’s birth/baptism records in Army and/or Army Chaplain’s returns of births. They for part of the GRO’s overseas BMD’s; I don’t think they are available on Ancestry but there are a few online pay per view sources and some UK main libraries hold copies. It’s possible they are listed in Non-conformist BMD records as they also contain overseas births/baptisms.
If you had listed their names it would have been possible for anyone with access to those records to look them up for you.