No, there are not more atoms, you can compare compounds that have the same number of atoms. For example, n-octane (C8H18) has an autoignition temperature of 220°C, while isooctane (also C8H18) has an autoignition temperature of 396°C.
As for why they autoignition temperature increases with the amount of branching, that takes a pretty deep understanding of what chemical reactions are occurring at ignition. How much organic chemistry have you had? Doing a Google Scholar search on chemistry of autoignition will lead you to several studies and explanations of the process.
In short, though, burning is a free radical process. As you raise the temperature of a molecule, you increase the possibility that you will see some homolytic bond cleavage, producing two free radicals. Once free radicals form, there is a lot of chemistry that the free radical species can undergo. The simplest reaction is that two free radicals can combine to form a covalent bond, and if it is the same two free radicals you formed in the beginning, there is no net energy change. The amount of energy absorbed to break the bond is the same as the amount of energy released when the bond is reformed. But there are other things that can happen. In particular, if there is oxygen present, the free radicals can react with oxygen, forming C-O and H-O bonds which are much stronger than the C-C and C-H bonds that were broken to form the free radicals. This releases more energy, and the temperature increases, forming more radicals, and so on. Runaway reaction. Ignition.
The free radical formed in the initiation reaction described above may also rearrange to form a more stable free radical, giving off more energy. This rearrangement creates branched structures, and since it is an intramolecular process rather than an intermolecular process, it can happen more rapidly than the processes described above, and at a lower temperature. However, the more highly branched the chain is to begin with, the less available this pathway becomes. This means that for less branched alkanes, such as n-octane, a lot of energy can be released by rearrangement, increasing the temperature more than for more branched alkanes, such as iso-octane, which have almost no rearrangement pathways available. This rearrangement process adds energy to the the system, starting the increase in temperature and the runaway reaction process at a lower temperature than is available for more branched structures.
I hope some of that made at least a little bit of sense.