Everything you say is correct. There's only one warning about buying tickets prior to a price increase, and that's about upgrading them once your trip starts. If you bought the tickets directly from Disney online (MDE, mail order, will call) or from a WDW ticket outlet, you would pay for the upgrade, plus the price increase you skipped.
If you bought your tickets from a discounter like
AAA,
Undercover Tourist or Mapleleaf, or if they were from The
Disney Store or they were old package tickets, you could avoid paying back the skipped price increase (and skip paying back the discount) by using the tickets at one of the theme parks first before you upgraded. Using those tickets raises their value to that day's full gate price, and you'll just owe the upgrade cost.