More interesting for purposes of chronology is exactly when he dates the letters in Paul's life. There are three major candidates: authorship from Ephesus in the early 50s, authorship from Caesarea sometime c. 57-59, and authorship from Rome c. 60-62. Robinson rightly notes that the personalia of Ephesians, Colossians, and Philemon in particular indicate that they were written in close proximity to each other; the corollary is that while they should be placed in the same captivity, Philippians in principle could date to another. Sticking with those three, there is good reason to think that Caesarea is the place of origin. The personalia of these letters overlap significantly with those persons who according to Acts 20 accompanied Paul to Jerusalem for his fifth and final "Christian" visit, from whence he shortly thereafter was sent into captivity in Caesarea. It is easier to imagine this common personalia if the texts were written relatively shortly after the beginning of Paul's captivity in Caesarea than it is to imagine that they were written three or so years later (Paul probably arrives in Jerusalem around May of 57, and in Rome perhaps March or April of 60). This positive argument is compelling. In addition, Robinson argues that Paul's expectation that he would shortly be traveling through the Lycus Valley (the apparent destination of these letters) fits better with what we know of his plans during this period: he is consistently looking westward, and thus the expectation that he would travel westward from Caesarea by way of Asia Minor towards Rome makes better sense than the expectation that he would travel eastward from Rome. Rome however cannot be properly speaking ruled out. For its part, the strength of the Caesarean hypothesis and the possibility of the Roman virtually exclude the Ephesian, as we have no real reason to even think that Paul was captive in Ephesus in the first place. When it comes to Philippians, Robinson again argues that the Caesarean hypothesis seems strongest. His major piece of evidence here is Phil. 1:13, which associates Paul's captivity with a praetorium: precisely where Acts 23:35 tells us that Paul was imprisoned in Caesarea. Nowhere but in Caesarea are we able to put Paul in captivity in a praetorium.
As such, Robinson dates the prison epistles to 58, in the middle of the Caesarean captivity. In my judgment, he's probably spot on, but neither he nor I would rule out Rome c. 60-62 as a possibility.