When it comes to security, assurance generally comes in the form of insurance. There are no guarantees of perfect safety in any security system whether computers are involved or not.
After a cursory glance at the product you are curious about, it appears that they offer services such as taking screenshots of what is happening on your computer so you can tell what the thief is doing. This means that the company has to have access to at least the portions of your computer that connect to the Internet and take screenshots. It is likely that they are also doing more under the hood, which means accessing additional parts of your computer. Whether or not they will only do this when you ask them is a matter of trust. Does this company have a good reputation? Do any of the reviewers seem technically and/or security inclined? Is the content of your computer something that could compromise just your pride, or your safety? At the end of the day, it is you, the computer user, who decides if this company is trustworthy enough. Any anti-theft software that communicates with the parent company (or anyone via the Internet) should make you stop and ask yourself the same questions.
As for the second part of your question, no. This product is for anti-theft, not general computer security. If you are concerned about third parties compromising your system you should look into security software, blocking third party cookies in all browsers, regularly updating all passwords you use, etc.
You mentioned that your last computer was burgled. While it is far from a guarantee, always register your Apple devices with Apple. Usually the police cannot find the stolen goods and the owners are out of luck. However, in the off chance that the police do find the goods and no longer need them for evidence purposes, Apple is good about connecting the serial number with the original owner. I have known a handful of people who have been reunited with their iMacs, iPhones, etc. one and half to two years after the theft.
Also look into a laptop lock, which is similar to a bike lock. Most desktops also have a slot which can be used to lock them to a desk. If a thief is serious and prepared, they can cut through the lock. However, the vast majority of security is making something such a pain to access that the hacker/thief doesn't think it's worthwhile to pursue.