If it's going all over the wheel/tyre, you are doing it wrong.
First thing I do is put some scrap cardboard on the ground under the chain.
I clean the chain using a bit of cloth with some diesel on it, then wipe clean with a dry cloth.
Then I carefully spray Muc-Off Dry Lube onto the inside of the lower run of the chain, while rotating the wheel backwards. I start with the joining link visible on the rear sprocket and do one slow complete rotation of the chain with the spray going onto the left of the chain rollers, then another on the right of the chain rollers. I also take the opportunity to make sure there are no tight-spots in the chain. When I first fitted the chain, I painted the outside plate of the joining link red. This also helps me to see that the link is intact.
I then leave the bike to stand until the Dry Lube is dry (clue is in the name), and carefully dispose of the card and the cloths.
If you do have to lube the chain immediately before a ride, then Silkolene Racing Chain Lube is the product to use, as it is fling-resistant even when first applied. It's branded as race lube because you can use it between races.
Most of the chain manufacturers actually don't recommend chain lube at all...they say to use a heavy gear oil: an SAE EP90 or similar...the kind of stuff that used to go in Ford Cortina drive axles back in the day.
If you've got a decent chain, then most of the lubrication happens behind the O X or Z rings, the main function of the applied lube is to stop it all going rusty.
Below is my chain. It's done several thousands of miles of road and trail riding in all weathers, and the bike had just done 60 miles on damp country roads when I took the pic.