It's called post-void dribbling, and yes, it is a muscle tone issue that tends to increase as a problem with age. Milking the last drops out as Gymrat suggests is one solution. Kegel exercises in general improve the tone of all the pelvic floor muscles, including the ones that when relaxed allow the urethra to hold a tiny amount liquid instead of being more tight and collapsing flat.
Like any elastic substance, such as the soft tissue of your body, age will reduce skin tone, muscle tone, etc. all leading to a little sagging and bagging.
The more effort you put into muscle and skin tone, the less of the issues related to those slowly drooping tissues will be evident.
Caffeine will certainly affect your urinary frequency. The chemicals in soda will also have your kidneys working to balance your body fluid chemistry and creating urine too. Sodas are designed to make you more thirsty (anything sweet will), and therein seek more (soda) to quench the additional thirst. If you drank the same amount of plain water, the experience would be less dramatic.
If you find that you urinate too often, it can also be poor muscle tone that registers the trigger in your bladder that it's "time to go" when your bladder is not actually full.
Drinking half a gallon of water a day (about the right amount for adults), there shouldn't really be any urgency to urinate more than 3-4 times per day. Half a gallon is only two bladders full. The trigger to urinate can start as early as 25% full. Even at half full, that's still only 4 trips to the bathroom.
That said, don't hold it in when you have to go. Fighting the urge can lead to other problems.