Your laptop or phone does not walk the DNS tree itself. It sends the question to a recursive resolver, usually one run by the internet provider, the company network, or a public service, and waits for the final answer. The resolver starts at the root servers, is referred to the servers of the TLD, then to the domain's authoritative nameservers, and returns the record it receives.
Resolvers cache every answer for the record's TTL, so the second person asking for the same name gets the answer immediately. This cache is also why two people can see different answers for a short time after a DNS change.
A validating resolver additionally checks DNSSEC signatures and refuses answers that fail validation. Resolvers may also apply local policy such as filtering, which is another reason results can differ between networks.