I am a travel agent and this is a really frustrating situation! I am very happy to help to clarify for you....
First of all, when they try to hand me a drink - I ask the waiter directly if this drink is complimentary. If they start to get pushy, just repeatedly and politely tell them, "No, thank you." I suspect that the cruise lines are trying to add to the atmosphere of excitement and anticipation at the beginning of the cruise with a fun atmosphere - some of the stewards can get a bit aggressive, but you can always refuse the drink. Generally speaking, anything beyond coffee, tea, iced tea, ice water, juices and milk are going to be added to your account. Occasionally, the soft drinks are complimentary in the dining rooms, but, again, be sure to ask!
Just be very clear before you board the ship and while on the ship about the drinks that are included in the price of your cruise. Anything with bright colors, fruit, umbrellas, wine or other alcohol is going to an additional cost. When I am on a cruise, I usually drink lots and lots of iced tea - it is a complimentary drink and is always available in the buffet on the ship. I find it very refreshing and a nice change from my usual soft drinks at home.
I encourage you to enjoy a nice glass of wine at dinner, a cocktail after a formal evening or for a special event, but prices on cruise ships are at a premium.
Have a great day!