1st thing to check, have you set the birthday channel.
If not the bot has no idea where to wish you a happy birthday and will not send it. Use
b!channel <#channel> to set that channel.
2nd, has that user set their birthday?
Have the user run
b!getbday and if the bot responds with "You have not set your birthday yet." Look at Commands to do so.
All birthdays will be announced at 12:00 noon in UTC. Once you set your birthday in one server with the Birthday Bot it will be announced in all servers the bot and you share.