I have installed the official MySQL package on my PowerPC Mac with Tiger, althought I have check in the preference pane the "automatically start server", it doesn't, I need to start it manually.
I had the same problem you describe when I installed MySQL on Tiger. When I looked it up, it turned out to be a common and known issue but not one which anyone seemed to be doing very much about.
I have since updated from Tiger to Leopard but haven't ever had much use for MySQL on my own computer so never bothered trying out the latest install of that. I thought I'd try installing it now anyway just to see if the problem had been fixed.
In the x86_64 dmg download, the problem still existed but I found the following link after having a look around the error report page. The linked file fixes the problem in Leopard:
I'm not sure if either of these would work in Tiger or even if you'd want to risk trying but I posted them here so that anyone using Leopard might see them and appreciate the info.
Basically, I haven't solved your problem since you're running Tiger but I hope you might find it reassuring to know that it seems to be a pretty normal thing to happen!
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In the x86_64 dmg download, the problem still existed but I found the following link after having a look around the error report page. The linked file fixes the problem in Leopard: