Time doesn't seem to fit the mind school. Probably better to leave it at arcane, or perhaps arcane plus water? Also, the time travel mechanics are kind of messy. Also, a quick action quadruple strike? That's a lot of strikes for only the cost of one quick action.
Personally, if I were to make a time mage, it would be more about changing how things move in relation to time. Make things faster or slower, use pseudo restraining effects (frozen in time) or pseudo-teleporting effects (moving so fast it's like everything else stands still) and maybe some kind of undo ability which has severe restrictions on it (like only being usable one or two times per game.)
Of course, irl time as we know it doesn't really exist, it's just another spatial dimension. In fact, you can even construct a map of four dimensional space inside your head just like 3d space. A growing or shrinking sphere, seen from a different angle, is a cone with a rounded tip and a rounded base. A sphere that is moving forwards in a straight line, seen from a different angle, is a cylinder with rounded ends. Etc.
And if you're treating time as just another spatial dimension, time-related abilities could be more fitting for a sorcerer, since it's been said that that mage will be focused on portal magic and teleporting and stuff like that.