I don't worry about the fungus.

It's best to mulch either before the soil gets cold in the winter or to wait until it warms up in the spring. If the soil is warm when you put the mulch down, the mulch will help it stay warm through the winter. If it's cold, the mulch will keep it cold longer.

The dog vomit fungus stuff appears mostly in woody mulches (I've never seen it in shredded leaves) when conditions are right, warm and moist weather. The appearance of this has nothing to do with when the mulch was plunked down. As bpgreen has stated putting a good mulch down on really cold soil can dely warm up, while plunking a good mulch down of overly warm soil will reduce the temperature, but will also help that soil stay warmer, longer in the fall.

Mulch will never hinder plants pushing their way thru the mulch. The plants can be very persistent. The mulch won't keep them down. This time of year, I am just itching to dig in the dirt and every day I check to see if any of my perennials have decided to peek thru the ground. Happy planting!

The USDA has a good enough article, see attached. You may want to google "time to mulch" you'll get an array of ideas. Personally I mulch when the mulch is available and I have time...i.e. after the leaves fall from the trees and we've had time to shred them. But this year I received a load of free top soil from the dept of transp and will use it to topdress my beds, then I will top that with what shredded leaves I still have. I live in the woods so I don't bother with wood mulches.

Here is a link that might be useful: USDA NCRS Mulching

I like to mulch when I can see the plants and when it isn't too hot (mulching is heavy work) - any time between, say, mid-spring and November.

My gardens are mulched with leaves over the winter. Last week I started to clean up and rake some (but not all) of the leaves back from the gardens. This exposes more of the soil surface to let it warm up faster, and prevents the bulb shoots from growing that weird yellow color under the leaves because they're not getting any sunlight. Also, this encourages the self-seeders to sprout and one thing I really enjoy in the Spring is poking through the garden to see what has self-seeded. Throughout the Spring, I am often transplanting seedlings or dividing perennials - sometimes even moving a shrub - and this is easier to do before mulch is applied.

Then, in later Spring, after most plants have gotten moved and settled, things are happily growing, etc. I'll lay down some shredded leaves and compost as mulch. I almost always do this after a good heavy rain, because that way the mulch will help to preserve moisture in the soil.

Mulches indeed can have a lot to say about how a plant might come into the world.
Mulches, if you understand what they do, one thing is they retain moisture longer.
In the spring, when the sun has not been so bright, the garden area maybe being shaded longer, the mulch in this case is preventing the soil from drying. The wet conditions of the soil may indeed affect the plant trying to come up.

The area still having lots of moisture, may be denying the under-soil from thawing as other nearby areas may be already.
Pulling the mulch back---and off---the area can drain better, can dry better and invites the sun to do what it does.

Then, when there is a need for mulch, to retain moisture, to retain the temperature longer, to deny sun to weeds, it is given back.

Depends what you're doing but the above posts have the basic wisdom. If you are mulching against erosion the general rule would be to cover the bare soil a.s.a.p. I tend to mulch when time permits. I just pulled back a few inches of matted leaves when outside temps were well above freezing and found frost and some ice beneath.