Couple of thoughts:
House Bjornaer section in HoH:M has special rules and explanation how they treat and handle apprentices.
House Jerbiton section in HoH:S has some great thoughts - e.g.: it is okay to kidnap children with the Gift - and they do use regular schools to find Gentle Gift kids.
The regular perception on a Tytalus Master abusing the Apprentice... must be quite well founded, somehow they do get their House Virtue. 
On the other hand, I would absolutely not expect a Tremere Master to abuse or fraternize their students. The training will be harsh and focusing on other useful abilities as expected from a Tremere, and most probably it will give significantly less rights - at the beginning - compared to other Houses' Apprentices.
Apprentice has to prove thyself and earn their rights. This can be turned to great story hooks as in a Tremere dominated Covenant, multiple students fight to earn their Master's approval and earn rights within the Covenant e.g. bear arms, command grogs, travel to the city, dine with the Masters, drink wine at the table and silently listen to their conversation.
I can easily imagine wide range of possibilities how a Verditius Magi could treat their apprentices and grant them rights.
General approach could be to turn them as soon as possible to an effective Vis gathering helping-hand... which would result in fast advance when can an apprentice command grogs, get his first shield grog... and treat grogs as tools, which is a great way to introduce Hubris.
Duty would call the Apprentice to collect Vis with some gorg company from the easy to reach and not-expecting-complications places (or even steal some) and could grant a senior apprentice the right to own Vis, which is anyway needed for the Masterwork.
Master's appreciation would highly depend on the Craft and Magical Theory, an apprentice brings to the (Laboratory) table. I do consider within the House Verditius it could be also a matter of prestige, how ones student first master work is done... not to forget it will be kept by the Master.
So I would say the Verditius Apprentice could have one of the most appreciated life in a Covenant, while at the same time they are required to focus and provide help to their Master's daily work. A senior Verditius Apprentice would have to learn how to handle merchants, agents... which on it's own is a right to earn.
He could have a couple of the Master's magical items (maybe some experimental ones too), just to make him really proud of being a Verditius... starting the whole Hubris business. Nevertheless a great way for a Vergitius Mage to show off.
On the other hand, if the apprentice is headstrong or extremely bright, I can easily imagine some extremely cruel treatment. Master could turn and realize how the apprentice could over-shine him, already in a few years, taking away potential customers, and start abusing or keeping the training at minimum.
For a Flambeau I would imagine the apprentice would gain rights over the Covenant's grogs quite fast or an area to watch over in the Covenant.
I wouldn't be surprised if the apprentice's standing/rights would be dependent if he/she has bloodied his/her hands or not.
Could you imagine a full fledged Flambeau Mage - after the Gauntlet - who collapses in shock, after the first Pillum of Fire charcoals a mundane?
The whole House would laugh... one has to maintain it's prestige.
A Bonisagus Apprentice would raise their Latin and Magical Theory quite fast at the beginning, both from lecturing and from books. Earning rights (can read certain books) and tasks (clean) in the Covenant's library at the beginning of his study. In a close knit covenant a Bonisagus Master can easily lend the Apprentice time to a Sodales, especially in the seasons when special abilities would be required to continue some experiments. Like for a Verditius Apprentice at a later stage he can earn his right to have his own small laboratory, without the right to experiment.
Generally speaking an Apprentice is a future Mage and a Master's standing within the Tribunal and the House can greatly change based on how he treats and how he shapes the Apprentice. Master cannot only focus on abilities and arts... that's fine but only half of the job. How capable the young-after-the-gauntlet Mage is going to be. How you can trust he will not turn to the Infernal or cause havoc.
When an Apprentice starts the 15 years period, he is but a child, when finishes he is an adult and will have a vote in the Tribunal. He will handle matters with the local church and nobles. Will have vassals (Covenant folk and grogs) and handle other Magi, his new Sodales. After Gauntlet the past-apprentice - new-mage will represent the House. If the Master handles it poorly the whole House suffers down the line, creating a deficiency means everyone your apprentice will tutor will have it.
I don't think being a Master is a 1 season per year job and an Apprentice has to get/earn more and more rights/responsibilities through the years.