Simply, our service provides media upload in the same way you would if you sat behind a tablet 24x7x365, or you hired an agency to manage your Instagram on your behalf (who would post for you, like any other agency!).
There are now a few different solutions available for users to upload media to Instagram. We're not going to name them all (obviously) but a Google search will no doubt uncover them.
One alternative that several services have put in place is to help you out by "pushing" the image to your phone at the allocated time (sending you a mobile notification) -- these mobile apps are handy because it means you don't have to email the photos to yourself or remember when to post things, however they don't really solve the problem, because you still have to log into Instagram yourself and post the image. Certainly an improvement for brands, but a long way from useful (in our humble opinion). But services like this (e.g. Later.com or Hootsuite) are something we can recommend to more budget-conscious customers who are happy to perform this additional work themselves. Typically these services are half the cost of ours, but involve at least twice the work to get things posted!
As we have stated previously, Instagram forbids media uploads via their API, and also forbids companies from reverse engineering what they call their "private API" (i.e. the sequence of internet calls that the app uses to upload images/video).
We automate the posting process 100% so once you've uploaded your image and scheduled it, you won't have to do anything when the time arrives...it's auto-magic! We do this through using physical phones using the official Instagram app - this means that it's the same as if you hire an agency to manage your Instagram (or to help you manage it). You can read more about how we work here.
There are also a range of services who have just reverse engineered the "private API" -- and in many ways, the solution is simpler, easier to maintain 24x7, and consistent (which also means cheaper). However with that comes a risk -- what you are doing is in breach of Instagram's terms, and also (arguably) the law in many countries, which forbids reverse engineering proprietary software.
As with whether you trust us with your password, the decision to use any service is up to you as the customer, and if you are highly price sensitive and not concerned if Instagram decides to 'crack down' on users using these services (as happened with Gramblr (a desktop publishing tool), which resulted in "shadowbanning" where all accounts' images would no longer appear in public search results after using the service (!)). As with many things in life, 'you get what you pay for', and part of what we believe comes with paying for Schedugram is trust and support from our team.
We would recommend our users (like anyone) conduct their due diligence about how a solution gets around the API limitation. Certainly there is some grey area -- for example, would using "virtualised" devices (i.e. not real) contravene the terms (the answer currently is unclear)? However anything that uses any form of reverse engineering or the "private API" is in direct contradiction with Instagram's terms and should be used with caution.
We obviously can't speak on behalf of other services about how they manage their service or get around Instagram's limitations. We have very deliberately taken a conservative approach, and other providers may be the same, or take a more risky approach. The decision as to what balance is right for your account is up to you!
You should also check out the features of different services – for example, we offer video scheduling, landscape/portrait uploads, our 'first comment' feature and (recently) tagging people within your images – many of these aren't provided by other providers, so if they are important to you, it might make a difference. We are continually investing into building out the most feature-rich platform on the market, so if there's something missing you're welcome to suggest it to us, and it might already be in development!
As a result, we're 100% transparent with how our service operates, and who is behind the service. We also believe in providing the absolute best customer service, and while we can't speak of other services' customer support, we think we do it pretty bleeding well, and work hard to make sure our users are satisfied with our service -- both those in a trial and those who are active customers.