The barracks between Barrack Road, Dryden Road, and Topsham Road were known as Topsham Barracks until about 1960, they were the Depot of the Devonshire Regiment until the amalgamation with the Dorset Regiment. It was also the basic training depot for those two, plus, Wiltshire, Berkshire, Gloucestershire, and Royal Hampshire Regiments, which formed the Wessex Brigade, known by the symbol of the "Wyvern" (mythical winged reptile with dragons head) Hence the name Wyvern Barracks.
I do believe that the Royal Artillery were at the barracks before the first world war. My wife has forebears who were RA and stationed there, another member of her family was a cavalryman and came there about the time you are interested in, he moved down from a barracks in Hounslow)
The Royal Artillery were also at Higher Barracks at some stage of the last century.