Nah it's a dry process.
The male (left) molts for one final time, in which he gets his sexual organs.
The little "legs" in front that aren't actual legs, but are called pedipalps have hard "bulbs". They use these bulbs(called Emboli) to draw up sperm that they lay down into a special web. They can store it in the emboli for many months or years. Depending on the life span of the Ultimate male, usually short.
For most genus of tarantula males will also gain "hooks" on their front legs, these hooks, known as Tibial Spurs are used to pin back the females fangs while he used his pedipals to insert his emboli with the loaded sperm into her epigastrial furrow, where her spermathecae are located. From what I can compare it to it's like her ovaries.
Tibial spurs
Emboli that holds sperm.
Spermathecae examples
What is really neat is each species of Tarantula have their own Emboli/Spermathecae shape. Like having 1 key for 1 lock.
Some can hybridize if they are very closely related, but mating naturally from Genus to Genus would seem almost impossible for most all genus due to the emboli not fitting in correctly.
She will develop eggs and use the stored spem to fertilze the eggs. Some species this can take as little as 14 days some 6 months.
When she is ready to lay eggs she will make a special web and lay the egg mass down, then she will ball it up and seal it shut.
The egg sac will be cared for and tended by mom until they emerge from the egg sac. Most species will develop in about 60 days, some alot longer.
There really is no leakage Mike, I swear !!