Beginning at the same time

Paravians and the type of dinosaur they are purported to have evolved from basal Tyrannoraptora, appear in the fossil record beginning at the same time.
The purported dinosaur ancestor is dated at the same time as the basal paraves. 

Quote

Scansoriopteryx (Paraves)

Temporal range: Callovian to Kimmeridgian, 165-156 Ma

Quote

Serikornis (Paraves)

Temporal range: Middle Jurassic, 165-162 Ma

These Paravians are dated at the same time (165 ma) as the type of dinosaur they are purported to have evolved from. For example with:

Quote

Proceratosaurus (basal Tyrannoraptora)

Temporal range: Middle Jurassic, 165 Ma

Proceratosaurus is a genus of small-sized (~3 metres (9.8 ft) long) carnivorous theropod dinosaur from the Middle Jurassic (Bathonian) of England.[1] It was originally thought to be an ancestor of Ceratosaurus, due to the similar small crest on its snout.[2] Now, however, it is considered a coelurosaur, specifically one of the earliest known members of Tyrannosauroidea,[3] the clade of basal relatives of the tyrannosaurs.[4]

So the actual fossil evidence has paravians and the type of dinosaur they are thought to have evolved from appearing in the fossil record beginning at the same time.

Proceratosaurus

http://www.nhm.ac.uk/resources/nature-online/life/dinosaurs/dinosaur-directory/images//reconstruction/small/Proceratosaurus.jpg

Epidendrosaurus

https://upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Epidendrosauruswiki1.png/260px-Epidendrosauruswiki1.png

For reference:
Notice the imaginary line running from Coleurosaur to Paraves. There is absolutely no fossil evidence for this.

http://science.sciencemag.org/content/345/6196/562.abstract