The only way to know whether adding triple phosphate to your tomato seedlings is a good idea is to test your soil. Phosphorus is one of the three main nutrients all plants need to be healthy. However, until you know the chemical composition of your soil, there is no way to know whether phosphorus is even necessary.

While not always true, most soils have adequate amounts of phosphorus. Add too much and the nutrient balance could be thrown off, putting the plant under stress. Also, excessive amounts of phosphorus have been linked to algae blooms that clog waterways and rob them of oxygen. While the small amount you might use would be negligible overall, every “negligible” amount adds up.

Several state universities have soil testing labs. Penn State and the University of Massachusetts have excellent labs. The results will tell you not only the nutrient mix of your soil but also show acid/alkali balance and make fertilizer recommendations. UMass can test for lead if that's a concern. You can find out more about the Massachusetts tests by going to https://ag.umass.edu/services/soil-plant-nutrient-testing-laboratory
Penn State will analyze soil samples if you send it in. Instructions and the submission form can be found here:
https://agsci.psu.edu/aasl/soil-testing/fertility/soil-fertility-submission-forms
Results can be confusing. If you have questions, your county extension office can assist you. You can locate your extension office: Yourcounty.osu.edu