There's no real easy way to do this. The problem here is that your file is a mix between a traditional "log" file (with timestamps existing between events) and a tabular (CSV) data format. This isn't a typical use, and therefore isn't well supported. A few thoughts/ideas listed below.
Modify the log-producing program to format so that there's one timestamp per row (line).
Pre-process the CSV file so that the timestamp repeats for each row. This would be relatively simple to do in Python, Perl, AWK, or whatever tool you prefer.
Allow Splunk ingest each chunk of tabular data into a single event; then use some search-time magic to split each event into multiple events--one per csv row. I know a wrote a custom search command a few years back that did this exact thing. (I may be able to find it lying around; I never got around to actually releasing it.) But this probably isn't the best answer and may not perform as well, depending on your use case.
There could be some other clever approaches to this as well, but most of them will be either a pain to implement, hard to understand, or have a serious limitations. I'd try options 1 or 2 first.