There is no specific length of time to follow a total body routine before progressing to split routines. The major difference between split routines and total body routines is the amount of overload placed on the muscles and the amount of time available to train.
The ACSM Guidelines for resistance training call for training the major muscle groups: legs, chest, upper and lower back, shoulders, arms, hips, abdomen, for 2-3 days per week with at least 48 hours of rest between each exercise session. The guidelines call for at least one exercise per major muscle group for 8-12 repetitions for 2-4 sets with at least 2-3 minutes rest between each set.
These guidelines are very general but do provide a good structure for where to begin a resistance-training exercise program. Doing a total body exercise will be extremely beneficial for a person with a goal of exercising for improved health or overall general conditioning; however, if someone has a specific goal related to a fitness outcome such as improved muscular definition for a specific body-part or a specific level of lean body mass then a total body workout 2-3 times per week may not be enough overload therefore a split training program of fatiguing different muscles everyday might be more effective.
Split training calls for using one or two muscle groups at a time in an effort to fatigue those specific muscles. The main difference between a split routine and a total body routine is time. If someone has a goal to increase muscular development (size, definition, etc) as well as the time to do resistance training for 45-60 minutes a day then a split routine might be an excellent option to develop the desired levels of muscle size and hypertrophy; however, if someone has a goal of performing resistance exercise to improve general health or they only have a limited amount of time to exercise ,then doing a total-body routine that uses all of the major muscle groups in one workout would be an excellent strategy to achieve that goal.