First, relax and be glad you have submissive dog rather than an aggressive one. Chimay used to have the same issue and she has grown/learned her way out of it.
Second, the original replies are well founded.
The vet said that Jasper should grow out of it, this is partially true. As dogs get older they typically become more confident and independent and thus not as submissive.
As I have never witnessed first hand the behavior, I will be forced to make some assumptions, many will be what Chimay displayed during her troubled period.
For the dog's behavior to change, the situation of greeting people needs to change, as it is always going to happen and should not be avoided. When there is a knock at the door Jasper will run to the door and become very excited. The door will open and new guest will reach down to pet Jasper, he immediately goes flat on the ground and pees. I suggest not welcoming people immediately into the home. When the knock comes, leash Jasper and inform your guest that you are coming out. This accomplishes two things, it changes the setting for the initial contact and also if Jasper does pee then it's outside. Next, instruct the guest to keep some distance between them and you + Jasper while ignoring Jasper. This is not an unfriendly action, just a learning zone. This distance will allow Jasper to see and smell the new person and learn that there is no reason to overreact. Jasper will be excited, calm him by having him sit and stay, if need be distract him with treats. Talk to the guest calmly and Jasper will learn that they are not a threat. Once relaxed, allow Jasper and guest to fully greet each other: first by slowly closing the distance between them; then allowing Jasper to sniff without gaining any attention from the guest; followed by the guest petting Jasper once he actually walks away from the guest having finished his sniff investigation.
Remember, it takes time and effort to change our habits, especially the bad ones. In training Chimay to not pee when I would come home, my wife would do the previous steps. Often I would "come home" 5 or 6 times in a day, even on weekends just so she could get practice.
There are also many games and fun activities that can increase a dog's confidence, feel free to search these out and enjoy them with Jasper.