Here's what you would need to do. Hook up your old iPad to iTunes. In iTunes select the iPad and under the iPad there is an item called "File Sharing". Click on that. In the "Apps" column, select Time Master. On the left hand side it should say "Time Master Documents". Highlight the "database.rsd" file, then click on "Save..." at the bottom and save it to your Desktop (or some other place you can find it easily.
On your iPhone (assuming that you have not entered any data on it yet, otherwise a Restore will erase that), do a Backup to Dropbox (DB). Open up DB and find the Time Master Backups folder. Look at the name of the file. It should look something like "Adam's iPad_551902566.rsd". Now take the backup file from above and rename it with the numbers, so it may look something like "database_55192600.rsd" (I like to round the number up just a little bit as it is the Date & Time). Then put that file into DB from your computer. Do a Refresh of DB in TM. The file should now be there and you can Restore that data to your new iPhone.