Note the line There has been one in that time: is missing.
##Markdown
##Example Heading
There has been one in that time:
[quote="DeanMarkTaylor, post:1, topic:1"]
anything here
[/quote]
##Expected Output

##Actual Output

##Additional notes
For the markdown without the [quote ...][/quote] placing text under the heading works as expected:
##Example Heading
There has been one in that time:
Some additional thing
Or placing a blank line before the [quote ...] line:
##Example Heading
There has been one in that time:
[quote="DeanMarkTaylor, post:1, topic:1"]
anything here
[/quote]
I tried this in dingus: http://spec.commonmark.org/dingus/
It gave unexpected results for all cases where a blank line wasn’t after the heading.