As
Nekojin points out, it is quite likely that the significance of the word "tips" is not derived from the phrase "to insure proper service" - it's
etymology most likely lies in a more mundane explanation:
With reference to Webster 1913's entry, the phrase "to tip the wink" uses the word "tip" to mean "to give". Along the same lines, a commonly used phrase in Britain was "to tip up" for something, such as a round of drinks for example. This also means "to give" or "to pay".
It is believed that the use of the English word "tip" to mean "gift" is derived from the Latin word stipis, which means "gift".
See: stipend