For each motif it identifies, STREME first makes a list of the highest scoring occurrence of that motif in each of the training sequences. Then, by default, STREME takes the sequences in training set, center aligns them, and trims them to their longest common length. STREME then walks through each position in the aligned sequences and counts how many of the sequences had a motif instance at that position, considering only at the highest scoring motif instance for each sequences. The array of numbers in the site_distr element are the counts of those motif occurrences for each position in the aligned and trimmed training sequences. In the "Advanced options" for the web application you can choose whether the sequences should be center, left, or right aligned.
In command line version of STREME you can choose this via the '--align' option.