I went through this recently.
Short term disability for childbirth and recovery and provided through an employer typically works as follows:
1. You register with the disability insurance provider partnered with the employer. Usually they don't recommend registering sooner than 60 days before the due date because it is hard to know your medical circumstances far in advance. They will require that you submit proof of pregnancy...many times they'll contact the OBGYN office directly but sometimes the woman has to be the one to submit the form to the insurance company.
2. When registering, your wife will indicate her reason for the disability pay - in a normal birth, it will be listed as something like childbirth/recovery from childbirth/bonding with newborn. If she is having complications and needs to be off work before her due date, there is an option for that as well. Standard is 6 weeks of disability pay from the date of birth. Many employers only cover 40-60% of salary.
3. In a normal birth without a medical need to be off work beforehand, the disability pay kicks in after you give birth and never before. It is up to the parents to alert the company of the date of birth to start the payments. So when I gave birth, I just called the next day and told them I had given birth on X date, and they arranged for the payments to start that week.
4. The pay can be direct deposited if the woman provides this information to the insurer when she registers.
5. After 6 weeks, the deposits/checks stop.
6. In many cases, the insurer will provide a separate W2 for this disability pay so you can claim it appropriately when you file your taxes. If paid through the insurer, this income will not be reflected on the employer's w2.
7. Disability and FMLA run concurrently. For example: if your wife leaves work on April 20th, and gives birth on May 1, her FMLA will have started on April 20th and will run 12 weeks from that date. Her disability payments will start on May 1st or 2nd and will run 6 weeks from that date.
As far as her eligibility to receive the benefit, it depends on her employer. Typically, employees who have surpassed their probationary period (usually 3 months) and who are enrolled in the short term disability benefit are entitled to receive this. As others have mentioned, you are probably thinking of the year requirement for FMLA.
