If by "picture organization" you mean sorting, then you don't have much control over when pictures arrive at a receiver. Internet packages can take alternate routes from moment to moment to avoid bottle necks, so you can't know in what order they arrive. You can send them one at a time-- the pause between them allows the one you just sent to will arrive first-- seems awkward, though.
I don't know how Shutterfly decides the order. You can change the titles or the filenames so that they are in the order you want, and maybe Shutterfly can use that. To make sequential file names you would export the pictures

to a Finder folder and send them from there instead of directly from Photos. If you choose "FileName>Sequential" from the Export Dialog, then you can have their names in the same order as in the album they come from, and you can give them a unifying name:

(perhaps better than "picture # " …)
Or you can add more useful titles with indexing using a script from here:
Thematic Index to Photos for Mac related … - Apple Community
or with the 3rd party app
Photos Workbench.