In order to answer this question as accurately as possible, it is necessary to quickly explain what happens when you submit to IMAutomator. When you submit a bookmark to IMAutomator (and this will be similar for other tools that are added later), the details of your submission are stored internally and then submitted to each of the individual social bookmarking sites according to the schedule you have chosen - for example, one link per day.
So of course, the submission schedule is the first factor. No links will appear on external websites until IMAutomator has made those submissions. You can view the details of the submission schedule for each of your bookmarks and it will show you the date and time of the expected submission. Sometimes the time can vary slightly but not by much.
When IMAutomator makes a submission to an external site, that submission is immediate - the link is live straight away and you should be able to go to the site and see your bookmark. Click on the list of supported sites to see the URL's of the sites that are currently reported. Each of them works a little differently but most have a link that shows the newest bookmarks that have been submitted so you should see yours there.
Once the bookmark has been submitted to the external site then it is up to the search engines such as Google to crawl those sites looking for the bookmarks and extract the backlinks to your pages. This is the part that we have no control over and cannot give you a time estimate for. Generally speaking, Google crawls sites that it 'likes' more freqently than others so some of those bookmarks will show up as backlinks within a day or two of being submitted.
Finding those backlinks is a little tricky as they are not always published by the search engines! Two good places to look are:
1) Yahoo Site Explorer
Go to http://siteexplorer.search.yahoo.com/ and put in your desired URL and this will begin to track that URL for backlinks. Some of the social bookmarking links will appear here.
2) Google Webmaster Tools
To use the link checker that is provided by Google, you first need to create a Google account and then access Google Webmaster Tools. You will need to add your site and verify it (instructions are provided) before you can start tracking. You then have at your disposal a number of useful tools including a list of links that point to your site.
Unfortunately Google only provides a 'sampling' of the links. As far as we are aware, there is as yet still no reliable way to list 100% of the backlinks to a site. Annoying we know!