Okay so I spent probably 30 minutes working on this problem tonight,
Finally I gave up and went online for the answer - shamed me to do so but even the hints weren't making sense to me.

But seriously? 59 can't possibly be the right answer?

Is it just me or is this mathematically incorrect?

 A glass jar holds a single germ. After one minute, the germ slits into two germs. One minute after that, the two germs each split again, forming a total of four germs. Continuing at this rate, a single germ can multiply to fill a whole jar in exactly one hour. Knowing this, how long in minutes would it take to fill the jar if you had started with two germs?

No, the jar won't fill up twice as fast, you only save the one minute that required the first germ to split into two. So, the answer is 59 minutes.

In a funny puzzle way, it kinda sorta makes sense. But it's all wrong mathematically, amirite?

Not really...it takes an hour for the bottle to fill if it starts with one germ...and every minute is doubles...so when you start with two germs you are skipping over that initial minute for one germ to split into two...there are 60 levels to fill the bottle. Each level is a minutes so it would take 60 minutes, but since the questions asks how long it would take if you started from level 2...you take 1 away and get the 59. If that makes any sense at all :P

Well, I get that but wouldn't it be correct to just be 30?

So for like, if you're starting with 1 germ.
minute 1 = 2 germs
minute 2 = 4 germs
minute 3 = 8 germs
minute 4 = 16 germs
minute 5 = 32 germs
minute 6 = 64 germs
minute 7 = 128 germs
minute 8 = 256 germs
minute 9 = 512 germs
minute 10 = 1024 germs

So if it takes 1 hour to fill, and the germs generate 1024 germs every 10 minutes, then it should fill up at 6144 germs.

If it starts at 2 germs instead of one however..
minute 1 = 4 germs
minute 2 = 8 germs
minute 3 = 16 germs
minute 4 = 32 germs
minute 5 = 64 germs
minute 6 = 128 germs
minute 7 = 256 germs
minute 8 = 512 germs
minute 9 = 1024 germs
minute 10 = 2048 germs

So if it generates 2048 germs every 10 minutes, and the jar fills up at 6144 germs then..
The correct answer should be 30 minutes.
3 * 2048 = 6144.

Blah.

I guess I'm just pissed off because this was one of those "lol think outside the box" puzzles.

Edit:
After looking back at this - I'm not wrong.
This is redunkulous.
Ask the question, how many germs should you start with if you wanted to fill the jar in 30 minutes?

You are very mistaken in your math. After minutes 10 you have 1024 germs. You wrongly multiply that by 6 to get the final number of germs. If you kept going in the sequence, after 11 minutes you'd have 2048, and then 4096, then 8192, etc. So by 13 minutes you'd already have way more than what you claim to end up with.

Okay now everyone has confused me. What is the real answer?

The answer is 59. All you're doing it starting one step earlier.

It's a poorly phrased problem, You need extra information. For example: 
1. Does each germ split only once? 
2. Does the germ die after splitting? 
 
If 1 & 2 are true, only one split and dies, then the final total is all that matters, therefore you only save one phase and 59 minutes is the correct answer. 
If  only 1 is true, only one split and lives, then you have a cumulative total which means that after 59 minutes the second scenario is still 1 germ short  therefore the 60th minute is needed to fill (and overflow) the jar. 
If neither 1 or 2 are true, germs live and prior generations continue to multiply, the the time is exponentially less = 1+2+6+18 etc 
 
My son has the program and the answer they want is 59 minutes therefore, in their scenario, the germs split only once and die after splitting ... this is not borne out by their explanatory illustration which appears after the puzzle.