If you read up on people who actually have "perfect pitch", it's more than just correctly singing the first notes of all your favorite songs without a reference. It has to do with "seeing" each pitch as a color in your mind. One of my friends actually has it, and I've picked his brain about it many times. I don't understand how he "sees" pitches, and he doesn't understand how I don't. He's the same way with math. He "sees" numbers and shapes as different colors. It's really weird, but it has helped him go far in life with his career (computer programmer/mathematician). He's also a kick-ass musician. He pictures melodies as a series of color schemes, and he can instantly tell you what notes are being played in a solo, and repeat it immediately after hearing it.
So, you probably don't actually have perfect pitch, in the true sense of the term, but you have a good memory for specific pitches, which is excellent to have as a musician. I sing often, and groups I sing with don't need a pitch pipe with me around. As for "perfect timing", I doubt that something actually exists. I have a few "key" tempos memorized, but I couldn't count off to you the difference between 120 and 125 successfully. Just like pitches, tempos CAN be memorized, but should only be relied upon if you're 100% sure you've got them down. It sounds as if you probably do, so kudos!