You can save and use them. But the amount of EXP you can get "per chunk" is limited (I think the maximum you can get per chunk is one level and 95% into the new level).
Let's say you have 400/400 Siroma and 400/400 Roween, then you'd receive four chunks of EXP (1x base EXP for Siroma, 1x job EXP for Siroma, 1x base EXP for Roween, 1x job EXP for Roween). If you'd be a level 20 character and VIP, you could ask for base EXP only:
1x base EXP for Siroma -> level 21, 95%
1x job EXP for Siroma -> level 22, 95%
1x base EXP for Roween -> level 23, 95%
1x job EXP for Roween -> level 24, 95%
That would be your gain as VIP with four chunks at a low base level (the same for low job level if you put your EXP reward into job EXP only). Any EXP above 95% is lost. As non VIP you can get two chunks in that example (2x for base, 2x for job EXP).
Conclusion: save your TI reward, but use it once you're higher (base/job) level. Some people use it to get to job 50 (High Aco), some people use it to get to base level 85 quickly (so you can join 85+ TI parties), some people might save up the EXP for something else. You can use the wiki EXP chart to see how much EXP is needed to gain a level (and 95%), compare that to the EXP one chunk would give you and see if you'd lose EXP or not.