It's all in the dates. For the $3.60 charge if you look at the dates for that usage it's 6/25-6/25 --- so the text package was only effective for one day, the end of your bill cycle, so for that 1 day you were only allowed 16 messages. So the allowance was prorated because the package was only effective 1 day. Going forward though you're given the full allowance because the package will be effective for the whole month..so you're not limited to just 16 messages per day... you have 500 messages per month.
According to what you have listed there, it looks like you did an on demand feature change which caused you to have a prorated charge and allowance for the 25th. For the 25th, you used 51 text messages, but due to the on demand prorations, you were only allowed 16. The full package started over on the 26th.
If you called in to Customer Service, they should have backdated you to cover your texting and prevent overages. This is an error on their part and you can receive a credit for the balance. However, if you made the change yourself through My Verizon and did it On Demand, then these are valid charges.