When you search, the results are transactions which contain the matching search term. For transactions with splits, then, you still have to click to open the transactions to see the splits, or set your Settings > Register to Automatically Show Splits in Register.
If you're trying to figure out the total amount of transactions with a given string in the memo field, I'm not sure there's a good way to do that. You might want to switch to using tags instead; if you tag one line in a split, you can do a Transactions by Tag report and it will only include that one line item & not the whole transaction.
I'm not sure I understand your last post. One of the significant shortcomings with Search is that it finds all transactions containig the search term, and so for transactions with splits, the entire transaction amount rather than just the matching split amount is included in the Search total.
If you can construct a Report to find the data you want, Reports contain the individual split lines rather then parent transactions. So if you can base your query on Tags, a Report should be able to get what you want. But if your query is based on text in a Memo filed, there's unfortunately no way currently to use that as a criterion for a report. there is a long-running Idea thread on this site asking for that functionality to be added; I suggest you take a second to add your vote for the Idea.