Hi. I am not sure why you are naming this an umbrella tree. Most plants with that name are a house plant known as schefflera. This looks like mulberry tree, a weedy tree. Can you give me some details about where it came from? If it was in my yard I would remove it. If you want to keep it, remove ALL fallen debris as the leaves drop and discard them. While the tree is dormant prune out some of the branches to increase air circulation next summer. Many plants and trees developed fungal issues late in the summer because of high humidity and warm temperatures. I doubt whether the problem will return next year.

Hi again. Another responder has passed on a comment to me about your tree. Could you tell me if this is a weeping ornamental tree?

Hello.  My apologies for not responding earlier.  There has been a couple of pressing family issues.  You are very perceptive.  What I refer to as "umbrella tree" IS really a weeping male mulberry tree...... a  Morus  alba chaparral.  Your response says "not to worry this year ....... but still concerned WHY the fungicide that I used was ineffective.  IF the spots are a "fungus," please recommend a protocol for proper prevention next season.  Thank you for your input.

Fungicides are best used as prevention. Once the spots are present on the leaves a fungicide will not 'cure' it. The best method to control it is to use integrated pest management (IPM) strategies. This fall be sure and clean up and dispose all the leaves that fall from the tree. During late winter when the tree is dormant look at the shape of the tree and prune out some branches to allow for better airflow. If you choose to use a fungicide it is important to cover the leaves entirely--top and bottom. Follow the directions on the label, it may be necessary to reapply at certain intervals or after a rain. Since weather conditions play such a big role in the development of fungus I highly recommend the IPM approach to keeping your tree healthy next year. Also, your tree will be healthier if you remove mulch, rocks etc from the base of the tree. You want to see a gentle slope - the root flare, not a telephone pole shape entering the soil.