The age of mushrooms and Pseudomonas is estimated. The rest is commonly accepted based on fossil evidence.
Pseudomonas bacteria existed around 700 million years ago in some form. They acquired their polar flagella about then which evolved into ATP production allowing animals to produce motion through a speeded up biochemical process.
Cyanobacteria would have moved onto land as soon as clay became available 539 (sometimes shown as 541) million years ago. But the clay would not have left fossil evidence, so paleontologists assume nothing happened on land at that time.
The numbers are constantly changing in science; so older information uses different numbers from newer numbers. The Cambrian explosion of life used to be said to have occurred 541 mya; and now it is said to be 539 mya. The transition when dinosaurs died out used to be said to be 65 mya; and now it is said to be 66 mya.
