A good SEO agency will build backlinks to your site slowly over a few months instead of too many links in a single month. There is nothing you should worry about if the links your SEO agency build is from a relevant and high quality site that is not associated with links that may be considered a “bad link neighborhood” (bookmarking websites, un-moderated directory sites, etc).
You should be building high quality authoritative backlinks to your website rather than focusing on getting as many backlinks as possible to your website. You need much lesser authoritative links to outrank a site with 10,000 links from spammy sites. New site must not build the links too fast because the search engine will consider this as spam and drop your ranking. If your site has less than 100 inbound links and you build 1000 links to it suddenly in one month, you will see a significant drop in the search engine ranking. The best way to build backlinks is to do it slowly by adding only 5 links per month. You can increase the number of backlinks gradually over time.
If your site has more than 100 inbound links, there is no problem if you build 50 links in a month. It is hard to build more than 50 links manually unless you are generating them with an automated software or you purchase them. It is not a good practice to build backlinks too fast because you will get penalized by the Penguin algorithm. The penguin algorithm is specifically looking for low quality links in an irrelevant content or use anchor text that are rich with all kinds of keywords.
If you are trying to build the links at a fast rate, the analytics will show that your site is not getting any search traffic from the search result. This will last for a couple of months but everything should recover after 3 months. If you did not see any increase in the search traffic, it is likely that your links are low quality. It is important that you fix these problems quickly once you notice it from your analytics so that you can recover back the traffic in the next search engine update.
Most people will direct the link to the homepage but it will be better to get the backlinks spread out in between the homepage and internal pages. The reason is that it does not look natural if all your backlinks are pointing to the homepage. Usually, people will link to a specific page instead of the homepage so you should focus most of your backlinks on the internal pages. You can direct the backlinks to your homepage in the first couple of 3 – 4 months. After that period, you should focus on getting high quality backlinks to the internal pages.