Smokey starts

Have you checked your chimney cap?

Your draft is not good, or chimney is plug up. The draft is weaker at the startup and warmer weather. But that's what happens when a screen is mostly plugged up. Once you get a hot fire going it pushes through the screen.

As mentioned ... either your chimney needs to be cleaned and/or you are having draft issues which are common in the fall and spring for many folks when outside temps are not quite as cold.

Are you sure the baffle is put back together correctly? That front baffle retainer can be difficult sometimes, especially if you haven't done it a few times.

Here are few things to try:
1. It's always mentioned here to open a window before lighting to even out the pressure in the room to stop the back drafting that is happening. What I have found with my two story home, if I open a window in the top floor (verses the room where the wood stove is located), it evens out the pressure in the house a lot better.
2. I have experienced smoke in the room just as you have on initial light. I started using an electric heat gun ($15) to start the fire. Load the stove up with small dry splits and place some cold charcoal from your last fire butted up against the wood. Point the heat gun at the coals and they will ignite in about a minute or two. When they do get going, the heat gun creates a blast furnace effect that heats the firebox/flue in a hurry. Since I started using this method, I have reduced the smoke in my home to almost nothing.

Of course you really need to figure out why you are having the issue. In my case, I need to install a lining in the fireplace chimney when I can afford it..

Since there has never been a problem with smoke until the baffle was replaced, I bet something is out of place. I'd put money on it! Maybe a starling built a nest in the cap while the stove was down? It's that time of year.